Sun flare CAN be beautiful, Phillip! As far as the shot of the woman with the rectangular-framed eyeglasses: I'm not sure if a P&S digitial would have made a more-balanced photo out of that scene, but it's possible that the shot could have been exposed a bit differently, and then post-processed a bit to make a more-balanced photo. There are two basic ways to handle STRONG backlighting + open shade like that. First way is to expose for the open shade, and totally blow the background out to white/white-yellow...your shot is close to that, but yet SHE still needs a bit more exposure, to see detail in her eyes. If done in-camera, adding MORE exposure by slowing down the shutter speed, or by elevating the ISO a full stop value (say from 200 to 400 ISO) would totally blow out the background. The second way is to expose mostly for the brightest tones, meaning the background, and then in software to "lift the shadows" by adding "digital fill light" or "shadow recovery". A third way is to have a reflector below and in front of the subject, to actually ADD MORE "real light" to the person seated in the open, shaded area.
THe shot of the older woman is STRONG backlighting; the shot of your GF in open shade with the green lawn behind is not nearly as strong, and it is closer in exposure than the shot of the older woman.
Anyway...yeah...thing about shooting some "talls"!!!! And have fun, keep on enjoying the new 50mm lens. Shoot as much and as often as you can. And yes, as you said, lighting is super important in photography. Photography means "light writing" or "writing with light"...lighting is indeed a BIG component in photography.